Back to Nautical Basic Principles LORAN C Sat. Nav. Sys. GPS

Electronic System of Position Fixing

GPS Systems

A GPS receiver measures distance from the satellite to a receiver using the travel time of radio signals.

So we require:

Precise and synchronised clocks to measure the time difference

And any signal deterioration or bending due to atmospheric causes.

Imagine a satellite transmitting in space.

Then there will occur at different distances from the satellite a measured time difference in the arrival time of the signal from the satellite.

Therefore a receiver on the surface of the earth would by measuring the time difference between the departure of the signal from the satellite  and the arrival at the receiver, be able to make out the distance from the satellite.

But how is the receiver going to be informed that the signal has left the satellite. So the receiver has to be informed of the time. This requires the receiver to have a precision atomic clock.

The triangulation is done in the same manner as are all triangulation’s done. Thus if we assume that the satellite transmits in all directions including in space, then the signals from three such satellites will intersect at a point.

But for this to happen the clocks on the satellites as well as on the receiver have to be atomic clocks, with absolutely NIL error of synchronisation.

But if the clocks are not absolutely synchronised as is the case, since equipping all the receivers with atomic clocks would make GPS beyond the means of everyone.

The triangulation is done in the above way, taking into fact that the clocks are not synchronised and that the triangulation is IMPERFECT.

In this case then the signals from 2 satellites would intersect as above. And a receiver anywhere in space would be in the shaded area where the two signals overlap.

With this IMPERFECT clock system then, if the third satellite signal is made to overlap then there will exist only two points in space where the receiver is placed.

Out of these two positions are separated by hundreds if not in thousands of miles, additionally one may be in space while the other will be on the earth’s surface. This since the signals from all three are received on the surface of the earth.

Of course a fourth satellite signal would remove the discrepancy but since the triangulation is solved practically so the fourth signal is not needed for triangulation.

We have now seen that a position is calculated from distance measurements to at least three satellites.

Now the problem arises of measuring the distance to a satellite in space

This is done by timing how long it takes for a signal sent from the satellite to arrive at our receiver.

The Mathematics

In a sense, the whole thing boils down to a “velocity times travel time” problem.

This simple equation is all that is used:

Velocity x Time  = Distance

In the case of GPS we’re measuring a radio signal so the velocity is going to be the speed of light 300,000,000 metres per second.

Synchronisation of Clocks:

The time measurements are extremely short.

If a satellite were right overhead the travel time would be something like 0.06 seconds.

The difference in synchronisation of the receiver time minus the satellite time is equal to the travel time.

Thus we require really precise clocks.

Even with precise clocks, what we require is a reference start time.

In a RADAR we get the reference from the time the signal pulse leaves the magnetron and the start of the sawtooth current in the CRT. There the time is synchronised. But for satellite signals, the Radio signals have reached a limit in speed.

So the problem in GPS is how to have a reference instant.

In the GPS system, if we have a reference instant then the receiver just has to measure the delay in the signal reaching the receiver from the satellite and it could then compute the distance over which the signal travelled.

The GPS satellites transmit something called a PRC. This PRC is also generated within the receiver at the same time.

The PRC from the receiver is matched with that received from the satellite and thus the receiver can easily compute the time delay, and thus the distance.

Rather than sending just any radio signal, the satellites send the signal as a code -  Pseudo Random Code”.

Or to be exact a ‘False Random Code’

Each satellite has a unique PRC

Why Random?

The Pseudo Random Code (PRC, shown above) is a fundamental part of GPS. Physically it’s just a very complicated digital code, or in other words, a complicated sequence of “on” and “off” pulses as shown here:

The signal is so complicated that it almost looks like random electrical noise. Hence the name “Pseudo-Random.”

PRC

There are several good reasons for that complexity: First, the complex pattern helps make sure that the receiver doesn’t accidentally sync up to some other signal. The patterns are so complex that it’s highly unlikely that a stray signal will have exactly the same shape.

Since each satellite has its own unique Pseudo-Random Code this complexity also guarantees that the receiver won’t accidentally pick up another satellite’s signal.

So all the satellites can use the same frequency without jamming each other.

And it makes it more difficult for a hacker to jam the system. In fact the Pseudo Random Code gives the US a way to control access to the system.

But there’s another reason for the complexity of the Pseudo Random Code, a reason that’s crucial to making GPS economical.

The codes make it possible to use “information theory” to “ amplify “ the GPS signal. And that’s why GPS receivers don’t need big satellite dishes to receive the GPS signals.

Each satellite transmits pseudo random noise spread spectrum signals on two different frequencies,

•L1 at 1575.42 MHz and

•L2 at 1227.6 MHz.

L1 carries the coarse/acquisition code (CA-code) and a precision code (P-code).

L2 usually only carries P-code, but could carry CA-code as well.

The CA-code is a short sequence that repeats itself every millisecond, is different for every satellite, and is known and open to anyone who wishes to receive and decode it.

The P-code, on the other hand, repeats every 267 days, and each satellite transmits a different seven-day segment before being reset.

The P-code requires a cryptological key to decode, which is limited to US Department of Defense (DoD) and other “approved users.”

This pseudo random noise can then be modulated, allowing multiple transmitters to use the same frequency.

Synchronising the receivers clock and the satellite clock.

If the clocks are not ticking in unison then there is no way the PRC can be compared for shift.

Since the entire GPS is based on time difference, the clocks have to be very good, because if the timing is off by just a thousandth of a second, at the speed of light, that translates into almost 200 miles of error!

On the satellite side, timing is almost perfect because they have precise atomic clocks on board.

And the receivers here on the ground?

Remember that both the satellite and the receiver need to be able to precisely synchronize their pseudo-random codes to make the system work.

If the receivers are equipped with atomic clocks (which cost upwards of \$50K to \$100K) GPS couldn’t be affordable.

However the GPS as we know of do not have atomic clocks, but the receivers still are able to measure time with an atomic clock precision.

The secret to perfect timing is to make an extra satellite measurement.

If three perfect measurements can locate a point in 3-dimensional space, then four imperfect measurements can do the same thing.

Using the 4th. Satellite signal to make a timing correction.

The 4th satellite gets rid of the imperfect intersection

Extra Measurement Cures Timing Offset

If the receiver’s clocks were perfect, then all the satellite ranges would intersect at a single point -position of the receiver.

But with imperfect clocks, a fourth measurement, done as a cross-check, will NOT intersect with the first three.

So the receiver’s computer finds that a discrepancy in time measurements.

So the receivers clock is not perfectly synced with universal time.

Since any offset from universal time will affect all time measurements, the receiver looks for a single correction factor that it can subtract from all its timing measurements that would cause them all to intersect at a single point.

That correction brings the receiver’s clock back into sync with universal time, and - you’ve got atomic accuracy time right on board.

Once the receiver has that correction it applies to all the rest of its measurements and gets precise positioning.

Thus all GPS receivers need to have at least four channels to make the four measurements simultaneously.

So with the PRC as a timing sync pulse, and this 4th extra measurement, the receiver is perfectly synced to universal time, and thus can measure the distance to a satellite in space.

However for the triangulation to work, the receiver needs also to know where in space the satellite is located.

The receivers start with zero knowledge—they don’t know where on the planet they are, or what time it is.

Because of this, a good signal from three satellites is required to determine:

•current time,

•latitude, and longitude, and

•a fourth to also determine altitude.

Most modern GPS receivers are capable of receiving on 12 separate channels.

P-code enabled receivers are able to benefit from having two different frequencies to lock onto.

This is used to measure the effect the ionosphere is having on the signals and helps improve accuracy even further.

Since the CA-code is only carried on one frequency, such measurements are not possible, so an estimate provided by the satellite is used.

Triangulation based on the CA-code is known as the Standard Positioning Service (SPS), with the P-code-based system being called the Precise Positioning Service (PPS).

Until now we have assumed that the position of the satellites is known, so we have used them as reference points in space.

But do we know exactly where they are? After all they’re floating around 11,000 miles up in space.

On the ground all GPS receivers have an almanac programmed into their computers that tells them where in the sky each satellite is, moment by moment.

The GPS satellites are constantly monitored by the US.

They use very precise radar to check each satellite’s exact altitude, position and speed.

The errors are called “ephemeris errors” because they affect the satellite’s orbit or “ephemeris.”

These errors are caused by gravitational pulls from the moon and sun and by the pressure of solar radiation on the satellites.

The errors are usually very slight but they must be taken into account.

Once the new position of the satellite is determined it is sent to the satellite which includes its new position  as an information packet with its timing signal.

So the position of the satellite is continuously updated at the receiver also.

Thus the PRC also contains a navigation message with ephemeris information as well.

As a GPS signal passes through the charged particles of the ionosphere and then through the water vapour in the troposphere it gets slowed down a bit, and this creates the same kind of error as bad clocks.

There are a couple of ways to minimize this kind of error. For one thing we can predict what a typical delay might be on a typical day.

This is called modeling and it helps but, of course, atmospheric conditions are rarely exactly typical.

Another way to get to these atmosphere-induced errors is to compare the relative speeds of two different signals.

This “ dual frequency” measurement is very sophisticated and is only possible with advanced receivers.

The GPS signal may bounce off various local obstructions before it gets to the receiver.

This is called multipath error and is similar to the ghosting you might see on a TV.

Problems at the satellite

The satellites also do have to account for some tiny errors in the system.

The atomic clocks they use are very, very precise but they’re not perfect. Minute discrepancies can occur, and these translate into travel time measurement errors.

And even though the satellites positions are constantly monitored, they can’t be watched every second. So slight position or “ephemeris” errors can sneak in between monitoring times.

“Geometric Dilution of Precision” or GDOP.

This depends on the number and the geometry of the satellites used.

If four satellites are clustered near each other, then one meter of error in measuring distance may result in tens or hundreds of meters of error in position.

But if many satellites are scattered around the sky, then the position error may be less than 1.5 meters for every meter of error in measuring distances.

The effect of the geometry of the satellites on the position error is called Geometric Dilution Of Precision (GDOP), which can roughly be interpreted as the ratio of the position error to the range error.

Imagine the tetrahedron that is formed by lines connecting the receiver to each satellite used.

The larger the volume of this tetrahedron, the smaller (better) the GDOP.

In most cases, the larger the number of satellites the smaller the GDOP.

Intentional Errors

The policy of “Selective Availability” or “SA” and the idea behind it was to make sure that no hostile force or terrorist group can use GPS to make accurate weapons.

Basically the DoD introduced some “noise” into the satellite’s clock data which, in turn, added noise (or inaccuracy) into position calculations.

The DoD may have also been sending slightly erroneous orbital data to the satellites, which they transmitted back to receivers on the ground as part of a status message.

US military receivers used a decryption key to remove the SA errors and so they’re much more accurate.

Turning Off Selective Availability

On May 1, 2000 the White House announced a decision to discontinue the intentional degradation of the GPS signals to the public beginning at midnight.

Civilian users of GPS are now able to pinpoint locations up to ten times more accurately.

Sources of Errors for a signal from the satellite:

Satellite clocks

Ephemeral

Atmospheric

Multipath

The GPS receivers use timing signals from at least four satellites to establish a position.

Each of those timing signals has some error or delay depending on the climatic conditions experienced before reaching the receiver.

Since each of the timing signals that go into a position calculation has some error, that calculation is going to be a compounding of those errors.

DIFFERENTIAL GLOBAL POSITIONING SYSTEM (DGPS)

The satellites are so far out in space that the little distances we travel here on earth are insignificant.

So if two receivers are fairly close to each other, say within a few hundred kilometers, the signals that reach both of them will have travelled through virtually the same slice of atmosphere, and so will have virtually the same errors

One receiver measures the timing errors and then provides correction information to the other receivers that are roving around.

That way virtually all errors are eliminated from the system, even if the Selective Availability error is brought in, it would be of no use.

The idea is simple. Put the reference receiver on a point that’s been very accurately surveyed and keep it there.

This reference station receives the same GPS signals as the roving receiver but instead of working like a normal GPS receiver it attacks the equations backwards.

Instead of using timing signals to calculate its position, it uses its known position to calculate timing. It figures out what the travel time of the GPS signals should be, and compares it with what they actually are. The difference is an “error correction” factor. The receiver then transmits this error information to the roving receiver so it can use it to correct its measurements.

Since the reference receiver has no way of knowing which of the many available satellites a roving receiver might be using to calculate its position, the reference receiver quickly runs through all the visible satellites and computes each of their errors.

Then it encodes this information into a standard format and transmits it to the ship receivers.

The ship receivers get the complete list of errors and apply the corrections for the particular satellites they’re using.

The Maritime and Port Authority of Singapore has set up facilities to broadcast differential GPS signal with effect from 9 Oct.1997.

The aim of providing the DGPS broadcast service is to further enhance navigational safety.

The service is free of charge

The DGPS service is provided via a marine radio beacon operating in the MF band at 298kHz at a transmission speed of 100 bps.

The system provides reliable all weather and round the clock DGPS data with 99% availability

The DGPS reference station of a channel dual frequency (L1 & L2) GPS receiver, a MF radio beacon transmitter, an integrity monitoring station, remote control facilities and back up facilities

The DGPS Reference Station is at a known fixed position and equipped with sophisticated GPS receivers.

The Reference Station would compare the positions received from its DGPS receiver with that of the known position and then generate DGPS data.

The DGPS data is digitally modulated, using Minimum Shift Keying (MSK), and output via a MF radio beacon transmitter.

The integrity monitoring station would verify the DGPS signals’ accuracy and ensure that the system provides timely warnings to the users if and when the system data should not be used.

The DGPS data propagates in the ground wave mode and the system is designed with a range of 200 km.

The positioning accuracy achievable ranges from ± 5 m to sub-meter accuracy, depending on the type of receiver used.

The DGPS signal could also be received inland, offering the same benefits to GPS users on land and in the air.

Technical Details of the

Differential GPS Reference Station

Station ID         : 65

Frequency        :298 kHz

Bit Rate            :100 bps

Modulation       :Minimum Shift Keying (MSK)

Data Format     :RTCM SC- 1 04 Version 2.0

Range               :200 km

Messages         :RTCM Types 9-3, 16, 3, 5 and 7

Facilities           :Integrity Monitoring, Remote Control and Back-Up facilities.

The navigation data message enables a receiver to calculate the position of each satellite at the time of transmission of the signal.

From this information, the user position co-ordinates (Lat/Long) and the user clock bias (error) can be calculated using simultaneous equations.  Four satellites are normally required to be simultaneously ‘in view of the receiver for dual-dimensional (3-D) positioning purposes.  The following paragraphs give a brief description of the GPS satellite signals and GPS RCVR operation.

The data includes information required to determine the following:

Satellite time of transmission

Satellite position

Satellite health

Satellite clock correction

Propagation delay effects

Time transfer to UTC

Constellation status

The navigation message is transmitted by the satellite on the L1 data link at a rate of of 50 bps.

It is made up of five subframes, subframe 1, 2, 3 contain 10 words, each word have 30 bits.

So each subframe being 300 bits long.

Subframe 4, 5 are subcommuated 25 time each.

Every subcommuated page has 10 words and 300 bits long.

Each 30 bits word contains 24 data bits and 6 parity bits, the parity bits can all be stripped, so every word may have 24bit (3 bytes) useful.

According to GPS standard position service (SPS) signal specification, the structure within the navigation message is as per following table:

Table 4. Navmsg

SUB    Total   Elapsed

FRAME           0          30        300                                          bits     time

1          TML    HOW   CLOCK CORRECTION DATA         300      6 sec.

2          TML    HOW   ephemeris of transmitting satellite I         600      12 sec.

3           TML   HOW   ephemeris of transmitting satellite II       900      18 sec.

4           TML   HOW   page “n” 0f 25 - messages,

ionosphere, UTC, etc                           1200    24 sec.

5           TML   HOW   page “n” 0f 25 - almanac,

health status, etc                                   1500    30 sec.

Note: The subframe ID number is part of the HOW word.

TML : Telemetry Message

Table 5. Telemetery message

One word = 30 BITS, 24 DATA, 6 PARITY

word    0          30                                300                  Total bits

1          TML    8-BIT PREAMBLE     24-BIT DATA             6-BIT PARITY

HOW : HANDOVER WORD

One word = 30 BITS, 24 DATA, 6 PARITY

Table 6. HANDOVER WORD

word    0          30                                            300                  Total bits

1          HOW   17-BIT TIME OF WEEK        7-BIT DATA   6-BIT PARITY

The NAV-msg is superimposed on both the P-code and the C/A-code with a data rate of 50 bits/sec.

The NAV-msg contains 25 data frames, each frame consisting of 1500 bits.  Each frame is divided into 5 sub frames of 300 bits each.

It will therefore take 30 seconds to receive one data frame and 12 ‘/2 minutes to receive all 25 data frames.

Sub frames 1, 2 and 3 repeat the same 900 bits of data on all 25 frames.

This allows the receiver to obtain critical NAV-msg data within 30 seconds.

This ensures that the receiver need not wait for a long period (12 to 15 minutes) to provide the first position.  It can do so within the first minute.

The data in the NAV-msg is normally valid for a 4 hour period.

The NAV-msg contains GPS system time of transmission, a Hand Over Word (HOW) for the transition from C/A to P-code tracking, ephemeris (almanac) and clock data for the particular satellite being tracked, and almanac data for all the satellite vehicles (SVs) in the constellation.

Additionally, it contains information such as satellite health, coefficients for ionospheric delay model for C/A-code users, and coefficients to calculate Universal Coordinated Time (UTC).

ACCURACY AND ERROR SOURCES

The following factors influence the final positioning accuracy obtainable with GPS:

The precision of the measurement and the satellite geometry.

The accuracy with which atmospheric and ionospheric effects can be modeled.

The accuracy of the satellite ephemerides.

GPS exhibits statistical accuracy distributions because of two important parameters, which are continuously variable.

(a)        The User Equivlant Range Error (UERE)

(b)        The Dilution of Precision (DOP)

UERE is a measure of the error in the range measurement to each satellite as seen by the Receiver.  UERE tends to be different for each satellite and tends to be at a minimum following an upload.